1. Tardigrade
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  4. Ice starts forming in lake with water at 0° C when the atmospheric temperature is -10° C. If the time taken for 1 cm of ice be 7 h, then the time taken (in hours) for the thickness of ice to change from 1 cm to 2 cm is

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Q. Ice starts forming in lake with water at $0^{\circ} C$ when the atmospheric temperature is $-10^{\circ} C$. If the time taken for $1\, cm$ of ice be $7\, h$, then the time taken (in hours) for the thickness of ice to change from $1\, cm$ to $2\, cm$ is

Thermal Properties of Matter

Solution:

$\because t \propto\left(x_{2}^{2}-x_{1}^{2}\right)$
For $x_{1}=0, x_{2}=1\, cm$ ,
$7 \propto\left(1^{2}-0^{2}\right)$ ...(i)
For $x_{1}=1\, cm , x_{2}=2\, cm$ ,
$t \propto\left(2^{2}-1^{2}\right)$ ...(ii)
Solving (i) and (ii), we get
$\Rightarrow \frac{7}{t}=\frac{1}{3} t=21\, h$